SOLUTION: A piece of wire (56 cm long) is cut into two pieces and each piece is bent into the shape of a square. If the sum of the areas of the two squares is 130 square cm, then how long wa

We start with this piece of wire:



We cut it into two pieces of length x and 56-x 




Then we bend the two pieces into squares, so that a side of each
square is th of the piece of wire, so we find the
sides of the squares by dividing the length of the piece of wire
by 4.



The area of the left square is  or  and the area of the right square is  or .

The sum of these two areas is 130 so we have the equation:



Multiplying through by 16









Divide through by 2



That factors as 



So there are two solutions

x=12 and x=44

However they are really the same solution because

if we use x=12 for one piece the other piece is 56-12 or 44 and
if we use x=44 for one piece the other piece is 56-44 or 12. So
the second solution is just the case where the larger piece or
wire were labeled x, and the smaller one 56-x.

So the shorter piece is 12 cm.

Incidentally the figures above are drawn to scale in accordance with
this problem!

Edwin